The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform

Q Wang - One of the best experts on this subject based on the ideXlab platform.

  • Vibration of carbon nanotubes studied using nonlocal Continuum Mechanics
    Smart Materials and Structures, 2006
    Co-Authors: Q Wang, Vijay K. Varadan
    Abstract:

    A nonlocal Continuum Mechanics model is developed and applied to study the vibration of both single-walled nanotubes (SWNTs) and double-walled nanotubes (DWNTs) via elastic beam theories. The small-scale effects on vibration characteristics of carbon nanotubes are explicitly derived through a complete Mechanics analysis. A qualitative validation study shows that the results based on nonlocal Continuum Mechanics are in agreement with the published experimental reports in this field. Numerical simulations are conducted to quantitatively show the small-scale effect on vibrations of both SWNTs and DWNTs with different lengths and diameters.

  • wave propagation in carbon nanotubes via nonlocal Continuum Mechanics
    Journal of Applied Physics, 2005
    Co-Authors: Q Wang
    Abstract:

    Wave propagation in carbon nanotubes (CNTs) is studied with two nonlocal Continuum Mechanics models: elastic Euler-Bernoulli and Timoshenko beam models [Philos. Mag. 41, 744 (1921)]. The small-scale effect on CNTs wave propagation dispersion relation is explicitly revealed for different CNTs wave numbers and diameters by theoretical analyses and numerical simulations. The asymptotic phase velocities and frequency are also derived from nonlocal Continuum Mechanics. The scale coefficient in nonlocal Continuum Mechanics is roughly estimated for CNTs from the obtained asymptotic frequency. In addition, the applicability and comparison of the two nonlocal elastic beam models to CNTs wave propagation are explored through numerical simulations. The research findings are proved effective in predicting small-scale effect on CNTs wave propagation with a qualitative validation study based on the published experimental reports in this field.

Gérard A. Maugin - One of the best experts on this subject based on the ideXlab platform.

  • Non-Classical Continuum Mechanics - Non-Classical Continuum Mechanics
    Advanced Structured Materials, 2017
    Co-Authors: Gérard A. Maugin
    Abstract:

    This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical Continuum Mechanics and generalized Mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, every entry is followed by a cross-reference to other related subject entries in the dictionary

  • What Is Classical Continuum Mechanics
    Advanced Structured Materials, 2016
    Co-Authors: Gérard A. Maugin
    Abstract:

    A clear-cut definition of non-classical Continuum Mechanics can be given only by a negation, so that we need recall what is understood (by us) by “classical Continuum Mechanics”.

  • What Is Generalized Continuum Mechanics (GCM)
    Advanced Structured Materials, 2016
    Co-Authors: Gérard A. Maugin
    Abstract:

    We classify under the title “generalized Continuum Mechanics” all what is not covered in the restricted framework of the Cauchy model exposed in the prerequisite Chap. 1 under the title of “classical Continuum Mechanics”.

  • Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century - Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century
    Solid Mechanics and Its Applications, 2016
    Co-Authors: Gérard A. Maugin
    Abstract:

    Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of Continuum Mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and Continuum modelling views. Chapters trace early works in hydraulics and fluid Mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on Continuum Mechanics is key: these provide the most valuable documentary basis on which a revival of Continuum Mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of Continuum Mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom Continuum Mechanics as a vividly evolving science still has its own mysteries

  • Geometry and Continuum Mechanics: An Essay
    Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century, 2015
    Co-Authors: Gérard A. Maugin
    Abstract:

    Geometry, analysis, and numerics all apply to a good modelling of continua. Mathematics is the natural language of physics (Galileo Galilei), geometry is the natural language of Continuum Mechanics. This essay emphasizes the more or less elementary notions of differential geometry that are hidden in the bases of classical Continuum Mechanics (Killing’s theorem, covariance, Riemannian curvature). Then it examines the intervening of more modern and sophisticated notions that have been introduced for pedagogical purpose in harmony with present day mathematics and others of which the need appeared in the twentieth century development of this science: connections, torsion, Cartan’s forms and spaces. The influence of Einstein’s theory of gravitation on this increased geometrization and the role played by the formulation of a geometric theory of evolving structural rearrangements and defects such as dislocations and material inhomogeneities is of prime importance. The main actors in this historical perspective appear to be Pfaff, Lie, Riemann, Killing, Cartan, Kondo, Kroner, Bilby, and Noll.

Vijay K. Varadan - One of the best experts on this subject based on the ideXlab platform.

S. Sivaloganathan - One of the best experts on this subject based on the ideXlab platform.

  • Brief Review of Continuum Mechanics Theories
    Fields Institute Monographs, 2019
    Co-Authors: Corina S. Drapaca, S. Sivaloganathan
    Abstract:

    The classical theory of Continuum Mechanics has its roots in the nineteenth century, in the foundational work of Augustin-Louis Cauchy, although its rigorous, modern development has been built upon Noll’s axiomatic framework which allows for a unified study of deformable materials. In the mathematical description of a material’s response to mechanical loading there are two important basic assumptions which form the foundation of Continuum Mechanics: (1) the mechanical stress at a given material point at time t is determined by the past history of the deformation of a neighborhood of the considered point (the principle of determinism and local action), and (2) the response of a material is the same for all observers (the principle of material objectivity). These principles are however too general to properly characterize the nature of specific materials and further simplifications of the relationship between mechanical stress and deformation are necessary. Such simplifications arise, for instance, from assumptions of infinitesimal deformations or for finite deformations that a material is simple, homogeneous, non-aging, has preferred directions of deformation, and experiences internal constraints, (like incompressibility, inextensibility, rigidity). In this chapter we provide a brief review of these concepts, as well as specific constitutive laws that have been used in brain research. In addition, we will present some modern theories that generalize classical Continuum Mechanics and may prove very useful in future studies of brain bioMechanics.

  • A Fractional Model of Continuum Mechanics
    Journal of Elasticity, 2012
    Co-Authors: Corina S. Drapaca, S. Sivaloganathan
    Abstract:

    Although there has been renewed interest in the use of fractional models in many application areas, in reality fractional analysis has a long and distinguished history and can be traced back to the likes of Leibniz (Letter to L’Hospital, 1695 ), Liouville (J. Éc. Polytech. 13:71, 1832 ), and Riemann (Gesammelte Werke, p. 62, 1876 ). Recent publications (Podlubny in Math. Sci. Eng. 198, 1999 ; Sabatier et al. in Advances in fractional calculus: theoretical developments and applications in physics and engineering, Springer, Berlin, 2007 ; Das in Functional fractional calculus for system identification and controls, Springer, Berlin, 2007 ) demonstrate that fractional derivative models have found widespread applications in science and engineering. Late fundamental considerations have led to the introduction of fractional calculus in Continuum Mechanics in an attempt to develop non-local constitutive relations (Lazopoulos in Mech. Res. Commun. 33:753–757, 2006 ). Attempts have also been made to model microscopic forces using fractional derivatives (Vazquez in Nonlinear waves: classical and quantum aspects, pp. 129–133, 2004 ). Our approach in this paper differs from previous theoretical work, in that we develop a general framework directly from the classical Continuum Mechanics, by defining the laws of motion and the stresses using fractional derivatives. The timeliness and relevance of this work is justified by the surge in interest in applications of fractional order models to biological, physical and economic systems. The aim of the present paper is to lay the foundations for a new non-local model of Continuum Mechanics based on fractional order derivatives which we will refer to as the fractional model of Continuum Mechanics. Following the theoretical development, we apply this framework to two one-dimensional model problems: the deformation of an infinite bar subjected to a self-equilibrated load distribution, and the propagation of longitudinal waves in a thin finite bar.

  • A Fractional Model of Continuum Mechanics
    Journal of Elasticity, 2011
    Co-Authors: Corina S. Drapaca, S. Sivaloganathan
    Abstract:

    Although there has been renewed interest in the use of fractional models in many application areas, in reality fractional analysis has a long and distinguished history and can be traced back to the likes of Leibniz (Letter to L’Hospital, 1695), Liouville (J. Ec. Polytech. 13:71, 1832), and Riemann (Gesammelte Werke, p. 62, 1876). Recent publications (Podlubny in Math. Sci. Eng. 198, 1999; Sabatier et al. in Advances in fractional calculus: theoretical developments and applications in physics and engineering, Springer, Berlin, 2007; Das in Functional fractional calculus for system identification and controls, Springer, Berlin, 2007) demonstrate that fractional derivative models have found widespread applications in science and engineering. Late fundamental considerations have led to the introduction of fractional calculus in Continuum Mechanics in an attempt to develop non-local constitutive relations (Lazopoulos in Mech. Res. Commun. 33:753–757, 2006). Attempts have also been made to model microscopic forces using fractional derivatives (Vazquez in Nonlinear waves: classical and quantum aspects, pp. 129–133, 2004). Our approach in this paper differs from previous theoretical work, in that we develop a general framework directly from the classical Continuum Mechanics, by defining the laws of motion and the stresses using fractional derivatives. The timeliness and relevance of this work is justified by the surge in interest in applications of fractional order models to biological, physical and economic systems. The aim of the present paper is to lay the foundations for a new non-local model of Continuum Mechanics based on fractional order derivatives which we will refer to as the fractional model of Continuum Mechanics. Following the theoretical development, we apply this framework to two one-dimensional model problems: the deformation of an infinite bar subjected to a self-equilibrated load distribution, and the propagation of longitudinal waves in a thin finite bar.

Marina Diaco - One of the best experts on this subject based on the ideXlab platform.

  • Geometric Continuum Mechanics
    Meccanica, 2013
    Co-Authors: Giovanni Romano, Raffaele Barretta, Marina Diaco
    Abstract:

    Geometric Continuum Mechanics ( GCM) is a new formulation of Continuum Mechanics ( CM) based on the requirement of Geometric Naturality ( GN). According to GN, in introducing basic notions, governing principles and constitutive relations, the sole geometric entities of space-time to be involved are the metric field and the motion along the trajectory. The additional requirement that the theory should be applicable to bodies of any dimensionality, leads to the formulation of the Geometric Paradigm ( GP) stating that push-pull transformations are the natural comparison tools for material fields. This basic rule implies that rates of material tensors are Lie-derivatives and not derivatives by parallel transport. The impact of the GP on the present state of affairs in CM is decisive in resolving questions still debated in literature and in clarifying theoretical and computational issues. As a consequence, the notion of Material Frame Indifference ( MFI) is corrected to the new Constitutive Frame Invariance ( CFI) and reasons are adduced for the rejection of chain decompositions of finite elasto-plastic strains. Geometrically consistent notions of Rate Elasticity ( RE) and Rate Elasto-Visco-Plasticity ( REVP) are formulated and consistent relevant computational methods are designed.